Belarusian world number one Sabalenka tamed 18-year-old American Iva Jovic 6-3, 6-0 in 38C temperatures on Rod Laver Arena in Melbourne.
In the evening, with the roof on because of the suffocating heat, 12th seed Svitolina stunned third seed Gauff 6-1, 6-2 as the American imploded.
Television images showed Gauff repeatedly smashing her racquet in the bowels of the stadium afterwards.
“Very, very pleased with the tournament so far,” said Svitolina, after inching closer to a maiden Grand Slam title aged 31.
The Ukrainian, who is on a 10-match win streak after a title-winning run at Auckland this month, added: “It means the world to me.”
Now into a fourth major semi-final, the former world number three will re-enter the top 10 in the rankings.
“It’s always been my dream to come back after maternity leave to make the top 10. Always been my goal,” she said.
For two-time Grand Slam winner Gauff, a decade younger, it was more Melbourne misery.
She has still never gone beyond the semi-finals at the tournament and the nature of the loss will sting.
Gauff’s serve deserted her, broken four times in the first set and twice in the second to leave her title aspirations in tatters.
Svitolina faces a severe test in Sabalenka for a place in the final.
The top seed is aiming to win a third Australian Open in four years and looks in ominous form, yet to drop a set.
Sabalenka is also on a 10-match win streak after victory in Brisbane.
“It was a tough match. Don’t look at the score, it wasn’t easy at all,” she said after overcoming the supremely talented Jovic at the start of a brutally hot day.
The match was played in fierce sun on Rod Laver Arena and just afterwards organisers closed the roof, ensuring far more comfortable temperatures.
The decision came after the tournament hit its maximum “heat stress” rating of five for the second time in four days.
Temperatures peaked at 43C outside so play on outdoor courts, which were to host junior matches, were put on hold.